Revisiting conventional noncovalent interactions towards a complete understanding: from tetrel to pnicogen, chalcogen, and halogen bond

Typical noncovalent interactions, including tetrel (TtB), pnicogen (PniB), chalcogen (ChalB), and halogen bonds (HalB), were systematically re-investigated by modeling the N⋯Z interactions (Z = Si, P, S, Cl) between NH3 – as a nucleophilic, and SiF4, PF3, SF2, and ClF – as electrophilic components, employing highly reliable ab initio methods. The characteristics of N⋯Z interactions when Z goes from Si to Cl, were examined through their changes in stability, vibrational spectroscopy, electron density, and natural orbital analyses. The binding energies of these complexes at CCSD(T)/CBS indicate that NH3 tends to hold tightly most with ClF (−34.7 kJ mol−1) and SiF4 (−23.7 kJ mol−1) to form N⋯Cl HalB and N⋯Si TtB, respectively. Remarkably, the interaction energies obtained from various approaches imply that the strength of these noncovalent interactions follows the order: N⋯Si TtB > N⋯Cl HalB > N⋯S ChalB > N⋯P PniB, that differs the order of their corresponding complex stability. The conventional N⋯Z noncovalent interactions are characterized by the local vibrational frequencies of 351, 126, 167, and 261 cm−1 for TtB, PniB, ChalB, and HalB, respectively. The SAPT2+(3)dMP2 calculations demonstrate that the primary force controlling their strength retains the electrostatic term. Accompanied by the stronger strength of N⋯Si TtB and N⋯Cl HalB, the AIM and NBO results state that they are partly covalent in nature with amounts of 18.57% and 27.53%, respectively. Among various analysis approaches, the force constant of the local N⋯Z stretching vibration is shown to be most accurate in describing the noncovalent interactions.


Introduction
Understanding noncovalent interactions is an essential issue due to their central role in supramolecular materials.Scientists have now oriented these weak intermolecular interactions in designing crystals and metal-containing compounds, 1,2 but they remain lacking experimental determinations of the interactions' characteristics themself.4][5][6][7][8][9] These interactions' families are generally characterized by the connection between a nucleophilic center Z, usually involving a specic molecule, and an electrophilic center, which could be an electron-rich region or a Lewis base.Alternatively, they can be described in other manners, i.e., s-hole interactions and charge transfer.
1][12] Chehayber et al. claimed three stable geometrical types of this dimer using ab initio MO calculations at STO-6G basis set, encompassing axial, equatorial, and square pyramidal structures. 11The NH 3 -SiF 4 TtB complex was reported to have some degree of covalency in the N-Si bond 11 but still be driven by electrostatic term. 10,114][15][16][17] In addition, a systematic work on TH n F 4−n -NH 3 complexes elucidated the factors affecting the TtB in detail was reported by Scheiner in 2017. 3he pnicogen family was rst discovered in the work of Solimannejad et al. 18 and rapidly attracted the interest of the scientic community because of its similarities with the earlyknown noncovalent bonds, i.e., hydrogen bond (HB) and HalB.3][24][25] Recently, Chandra et al. successfully demonstrated the superior strength of Cl-P/N phosphorus bond, overcoming the H-N/Cl in NH 3 -PCl 3 complex using matrix isolation infrared spectroscopy and theoretical calculations. 20Comparative strengths of TtB, PniB, ChalB, and HalB and contributing factors were assessed using ab initio calculations with the representation of third-row atoms (Ge, As, Se, and Br; respectively). 14However, for typical noncovalent interactions relating second-row atoms (Si, P, S, and Cl), to the best of our knowledge, there is no study systematically investigating their changes in geometrical structures, stability, and characteristics when going from TtB to HalB.
Different approaches could be, and oen are, simultaneously utilized to scrutinize the characteristics of the interactions in question.These methods are diverse in the descriptors used for characterizing as well as in the underlying theoretical backgrounds.Elgengehi et al. stated the good prediction in calculating interaction energies of noncovalent interactions can be made by high-order SAPT with the MP2 correlation and dispersion correction. 26Within the scheme of energy decomposition analysis, it was shown that the electrostatic force predominantly stabilizes the noncovalent interactions besides the supplementary contributions from other elements, i.e., dispersion and induction.8][29][30][31][32][33] This is critical because one can predict the strength of interaction of interest from information obtained either computationally through quantum mechanical calculations or experimentally via vibrational spectroscopies, given good descriptors are determined.In fact, local vibrational mode analysis, originally introduced by Konkoli and Cremer, is known as an in situ measure of bond strength. 34,64This has been employed in a series of works to assess the strength of noncovalent bonds quantitatively. 13,28,32,35Additionally, the chemical bonding within noncovalent complexes could be investigated by electron-density-based methods, such as Atom in Molecule (AIM) and NCI analysis. 36,37The utilization of such a variety of methods for studying noncovalently bonded systems oen raises the question of which descriptors are better at representing the interaction.In this context, it is necessary to conduct an investigation in which the characteristics of different types of weak interactions are elucidated systematically by different methods.
This work was performed to simulate these noncovalent interactions in a highly systematic manner with the aim of thoroughly discovering the electronic structures, and stability of NH 3 -ZF n complexes (Z = Si, P, S, Cl; n = 1-4), as well as providing a fundamental understanding of various interactions including TtB, PniB, ChalB, and HalB.The characteristics and relative strength of these interactions can be rationalized by utilizing different modern approaches to investigate the chemical bonding, i.e., NCIplot, high-order SAPT, local vibrational force constant, and also, the conventional methods of electron analyses (AIM and NBO).We highlight the agreements and disagreements between different approaches and provide corresponding explanations where possible.Ultimately, we propose the descriptors that best represent all the interactions of interest.

Computational details
The geometries of complexes and monomers were optimized at the MP2/aug-cc-pVTZ and B3LYP-D3/def2-TZVP level of theory.The B3LYP-D3 has been claimed to sufficiently describe the binding energy of noncovalent interactions, 39 while the TZ basis set by Ahlrichs and coworkers (def2-TZVP) 65 is recommended to give good results. 38The harmonic vibrational frequencies were then calculated at the same level to conrm if the structure is truly a minimum on the potential surface and as well as to obtain the zero-point energy (ZPE).Intrinsic features of a chemical bond, including changes in bond length, vibrational mode, and force constant, were analyzed to observe the effects of intermolecular interactions on involved covalent bonds in isolated monomers and to determine the characteristics of intermolecular interactions.Specically, the local stretching force constant derived from the local vibrational mode analysis theory was calculated to describe the strength of noncovalent interactions by using the LmodeA-nano code as a Pymol plugin. 40,41he values of binding energy (E b ) were calculated with optimized complexes and separately optimized monomers based on the supermolecular method.In addition, to measure the actual interaction occurring within a complex formation, the interaction energies (E int ) were determined by the energetic difference between the complexes and the isolated monomers adopted from the corresponding complexes.These energetic quantitative terms were corrected for the basis set superposition error (BSSE) using the counterpoise procedure 42 and ZPE.The extrapolation to the complete basis set (CBS) was based on the focal-point method, using the Helgaker equation: E(z) = E CBS + a exp(−bz). 43In particular, the MP2/CBS electronic energies were extrapolated from the single point calculations at MP2 and aug-cc-pVTZ, aug-cc-pVQZ, and aug-cc-pV5Z basis sets (abbreviated as aTZ, aQZ, a5Z).The DCCSD(T) correction term was calculated at the aTZ basis set.
The Atoms in Molecules (AIM) theory of Bader et al. 36 was used to analyze properties at the bond critical point (BCP) of the interactions formed and provide the topological graphs.These calculations were done at the MP2 density employing the AIMall program. 44The noncovalent interaction regions were quantitatively determined with the NCIplot 4.2 63 from the MP2/aDZ density at MP2/aTZ geometries.The 2D and 3D visualization of these interactions were plotted by means of Gnuplot 45 and VMD soware. 46The calculations of Natural Bond Orbital (NBO) 47 was performed at uB97X-D/aTZ level to elucidate the intermolecular interactions between NH 3 and uoride compounds (SiF 4 , PF 3 , SF 2 , ClF).The Natural Resonance Theory (NRT) was also applied to obtain their bond orders and partitioning into covalent and ionic contributions.Molecular electrostatic potentials (MEP) were computed at MP2/aTZ and analyzed on the 0.001 a.u electron density surfaces with the GaussView package.9][50] All quantum chemical calculations were carried out using Gaussian16 rev.03 program. 51he calculations of high-order SAPT2+(3) with MP2 correlated correction 52 were performed at the aTZ basis set via the PSI4 program to evaluate the contribution of different physical terms and the interaction energies of studied complexes.

Geometrical structures, molecular electrostatic potential and stability
The initial prediction of intermolecular interactions formed in complexes of NH 3 with ClF, SF 2 , PF 3 , and SiF 4 is based on the MEP surfaces at 0.001 e bohr −3 contours with the densities computed at MP2/aTZ (Fig. 1).The color ranging from red to blue indicates different values of potential which change from the most negative to the most positive, respectively.The V s,min and V s,max extrema values corresponding to the stationary points of these MEP surfaces are collected in Table S1 of the ESI.† The lone pair of N corresponds to the intense red region of NH 3 .This interactive site favors connecting with the blue part (positive potential) of SiF 4 , PF 3 , SF 2 , and ClF.The numbers of sholes characterizing these molecules are observed to decrease from 4 to 1, corresponding to the number of F atoms in uoride compounds.According to Fig. 1, all s-holes lie on the extension of the Z-F bonds (Z = Si, P, S, Cl).The MEP reproduction generally agrees well with the previous studies. 3,10,15,16,53,54emarkably, we found fully three s-holes of PF 3 in this work, whereas Alkorta et al. reported only two maxima of PF 3 but three for PCl 3 and PBr 3 molecules at MP2/aug ′ -cc-pVTZ level of theory. 19nterestingly, the surface minima in ClF anisotropically locate around the extension of the Cl-F bond as a strip and perpendicular to the axis of the Cl-F bond.These minima, however, do not t the position of the expected s-hole.This phenomenon results from these minima resonating with each other, which, in turn, creates a s-hole on the outermost portion along the extension of the Cl-F bond (ca.Table S1 †). 27,55he equilibrium geometries of targeted complexes at MP2/ aTZ, shown in Fig. 2, exhibit only one type of intermolecular interaction: N/Si TtB, N/P PniB, N/S ChalB, and N/Cl HalB.These N/Z formations (Z = Si, P, S, Cl) are conrmed by the existences of bond critical points (BCPs) and path bonds between N and Z atoms in their topological graphs (Fig. S1 †).Other less stable structures of these models are represented in Fig. S2.† The binding energies of investigated complexes are collected in Table 1, in which the performances of B3LYP-D3 method are also assessed.
For the TtB model, the calculations found three conformers of H 3 N-SiF 4 , including axial (Fig. 2), equatorial, and square structures (Fig. S2 † Regarding the PniB, the H 3 N-PF 3 equilibrium geometry obtained associates with the N/P bond length of 2.86 Å at MP2/ aTZ and agrees well with previous studies. 19,53In particular, the lone pair of NH 3 interacts with one s-hole in PF 3 , as predicted from MEP analysis.This geometrical structure was also pointed out as the ground state of analogous complexes of PCl 3 and PBr 3 . 19,20The calculated E b values in this work are −12.3kJ mol −1 at MP2/aTZ and −12.5 kJ mol −1 at CCSD(T)/CBS, which are less negative than that at MP2/aug ′ -cc-pVTZ (E b = −19.8kJ mol −1 ). 19Also, two hydrogen bonded conformers of H 3 N-PF 3 (structure II and III) are found (Fig. S2 †) but considerably less stable than the H 3 N-PF 3 PniB on the PES.
For the H 3 N-SF 2 complex, the global minimum on the PES is the staggered structure, in which the SF 2 molecular plane lies at the staggered position to NH 3 .It is worth mentioning that Otilia Mó et al. proposed the eclipsed structure to be the most stable structure of H 3 N-SF 2 . 56The re-calculations of two H 3 N-SF 2 conformers conrm the global minimum of staggered one (cf.Fig. S2 of ESI †).The E b value of staggered H 3 N-SF 2 complex at CCSD(T)/CBS is −20.4 kJ mol −1 , close to the value obtained at MP2/aTZ but less negative than that at B3LYP-D3/def2-TZVP by 5.1 kJ mol −1 (Table 1).
The H 3 N-ClF structure characterizes the bond length of N/ Cl HalB of 2.23 Å and the N/Cl-F bond angle of 180.0°atMP2/ aTZ.This N/Cl bond of H 3 N-ClF was previously reported as a conventional HalB with a negative (r 1 -r 2 ), where r 1 and r 2 are  ). 57he binding energies of typical noncovalent complexes in this study were also calculated using B3LYP functional with D3 dispersion correction of Grimme et al. 58 in conjunction with two different basis sets, i.e., Dunning type -aTZ and Ahlrichs type -def2-TZVP.From Table 1, both B3LYP-D3/aTZ and B3LYP-D3/ def2-TZVP do not effectively describe the binding energy of these typical complexes with respect to those derived at CCSD(T)/CBS extrapolation.The result thus does not agree with the observation found in CH 2 XOH-CO 2 (X = F, Cl, Br) complexes in which the B3LYP-D3 showed excellent descriptions of stability. 39ncredibly, the characteristic region obtained from MEP surfaces of the involved monomers completely ts the equilibrium structures found at MP2/aTZ.This implies a dominant role of Coulomb electrostatic force upon complexation.Since these complexes share the NH 3 host molecule, the maxima electrostatic potentials V s,max of electrophilic fragments, including SiF 4 , PF 3 , SF 2 , and ClF, are considered (cf.Table S1 †).Their V s,max decreases in the order of SiF 4 > ClF > SF 2 > PF 3 .However, the complex stability decreases in the order of H 3 N-ClF HalB > H 3 N-SiF 4 TtB > H 3 N-SF 2 ChalB > H 3 N-PF 3 PniB; this does not follow the decreasing trend of V s,max of Z central atoms (Z = Si, P, S, Cl).This inconsistency reveals that the binding energy cannot serve as an adequate descriptor for intermolecular strength.It can be claried by the calculations of interaction energies and the effect of the deformation energy in the following section, which reects the energy cost of involved monomers to bind each other and achieve the complex geometry.

Interaction energy analyses and energetic decomposition
The high-order SAPT approach is an effective alternative to estimate the interaction energy (E int ) of intermolecular complexes and decompose it into meaningful physical energy terms.Table 2 provides the E int values of studied complexes derived from various orders of SAPT and supermolecular methods.
Generally, the accuracy of E int according to the SAPT approach tends to improve signicantly with the increase of order with respect to that using the supermolecular method at MP2/aTZ.Specically, a high deviation is found between the interaction energies obtained from CCSD(T)/aTZ and lower order of SAPT calculations, e.g., SAPT0.By increasing the order of perturbation, the SAPT-based interaction energies get closer to those derived from CCSD(T)/aTZ.As a result, the SAPT2+(3) dMP2** approach exhibits an effective description of E int of noncovalent complexes (with the highest difference of only 4.0 kJ mol −1 in the case of H 3 N-ClF HalB, as compared to E int value derived from CCSD(T)/aTZ), and is consistent with the observation of Elgengehi et al. 26 The obtained interaction energies based on the supermolecular methods at three levels of theory, i.e., MP2/aTZ, CCSD(T)/aTZ, and B3LYP-D3/def2-TZVP, conrm again the ineffectiveness of the B3LYP-D3/def2-TZVP in evaluating the typical noncovalent interactions.The interaction energy of the TtB complex is signicantly negative, of −111.4 kJ mol −1 at CCSD(T)/aTZ and −109.81kJ mol −1 using SAPT2+(3)dMP2** approach while the corresponding E b is only −23.8 kJ mol −1 .This large deviation results from the withdrawing electron effects of three F atoms and the rearrangement of the SiF 4 geometry, leading to the substantial deformation energy in H 3 N-SiF 4 TtB complex (∼87.6 kJ mol −1 ) and in good agreement with an amount of 86.9 kJ mol −1 , reported by Scheiner. 3The high strength of N/Si TtB might be due to its partially covalent nature and will be claried in later sections.A similar trend was previously stated in the case of the HF 3 Ge-NH 3 complex. 14ased on Table 2, the bond strength of noncovalent interactions grows in the following order: N/P PniB < N/S ChalB < N/Cl HalB < N/Si TtB.This result is in line with the prediction of MEP analysis and differs from the trend obtained from the binding energies (Table 1).Therefore, the interaction energy should be a better bond strength descriptor in comparision with the binding energy.
The percentage of each component contributing to the strengths of noncovalent interactions unveils the nature of Paper RSC Advances noncovalent interactions (Fig. 3 and Table S2 of ESI †).The electrostatic term remains to govern the strength of complexes (53-63%), indicating that it primarily drives the strength of corresponding noncovalent interactions.The contribution of dispersion and induction terms are in ranges of 11-24% and 16-34%, respectively.The relative contribution of the exchange component to the total interaction energy typically increases when going from the complex with ClF to SiF 4 , with the absolute ratio E exch /E int(SAPT) rising from 3.21 to 5.39, respectively (Table S2 †).

Vibrational spectroscopy characterizing noncovalent interactions
In addition to the stability and energy decomposition, the intrinsic features of noncovalent interactions are further described through the changes in intermolecular distances and stretching frequencies engaged.The related adjustments of internal geometries, including the selected changes of Z-F a , N-H a intramolecular bonds (Dr) and local stretching frequencies (Dn), local vibrational frequencies of N/Z intermolecular interactions (n(N/Z)) and the corresponding force constant (k) are collected in Table 3.
The four typical noncovalent interactions are characterized by the elongations of Z-F a (Z = Si, P, S, Cl) and N-H a bond lengths, in ranges of 15-76 mÅ and 0.83-1.93mÅ, respectively, which initially reveal the weakening of the involving bonds Z-F a and N-H a upon complexation.The Si-F a bond length in H 3 N-SiF 4 complex is lengthened by an amount of 38 mÅ at MP2/aTZ, as compared to the original one Si-F in SiF 4 structure.This result is completely in line with the work of Scheiner et al. (0.037 Å). 3 Applied the characteristic proposed by Del Bene et al. to the investigated interactions in this work, 59 we also observed the negative value of (r(Z-F a ) − r(N/Z)), indicating they are all conventional noncovalent interactions.The stretching frequencies of Z-F a bonds shi to the red region with magnitudes of 47-216 cm −1 .This nding is typically similar to conventional X-H/Y red-shiing hydrogen bonds where X-H and Z-F a both belong to the electrophilic component, while Y and N act as the nucleophilic region. 60,61Especially, the N/Cl HalB formation encompasses a signicant shi of −216 cm −1 in n(Cl-F), conrming the strong effect of N/Cl HalB formation to the Cl-F covalent bond involved.
The local vibrational force constant is a reliable measure to examine the noncovalent interaction's strength directly, besides other methods of interaction energy.From Table 3, the formation of N/Z interactions is accompanied by stretching frequencies n(N/Z) of 351, 126, 167, and 261 cm −1 , with regards to TtB, PniB, ChalB, and HalB, respectively.More importantly, the k(N/Z) at MP2/aTZ increases in order N/P PniB < N/S ChalB < N/Cl HalB < N/Si TtB, conrming the strength order of investigated noncovalent interactions, as concluded from the energetic and MEP analyses.
The k of P/N PniB associated with the stretching mode at 126 cm −1 computed at MP2/aTZ is 0.009 mdyne Å −1 , signicantly smaller than the corresponding value of PniB in NH 3 -PH 2 NO 2 complex, which was reported to be 0.144 mdyne Å −1 (159.3 cm −1 ) at uB97X-D/aug-cc-pVTZ. 32 It is relatively consistent due to the remarkably weaker strength of NH 3 -PF 3 in this work (−16.7 kJ mol −1 for E b only corrected only BSSE and −12.3 kJ mol −1 for E b with ZPE + BSSE corrections) compared to that of NH 3 -PH 2 NO 2 dimer (ca.−31.63 kJ mol −1 , included BSSE but no ZPE correction, at uB97X-D/aug-cc-pVTZ).

Topography and electron density analysis
Table 4 summarizes some selected parameters at BCPs of these noncovalent interactions with the density obtained at MP2/aDT.The positive V 2 (r(r c )) values of all the considered interactions Fig. 3 SAPT decomposition of the total interaction energy of complexes between H 3 N with SiF 4 , PF 3 , SF 2 , and ClF at the aTZ basis set.indicate they are all closed-shell congurations.The r(r c ) at BCPs of Si/N TtB and Cl/N HalB are considerably higher than those of P/N PniB and S/N ChalB, conrming the higher strength of the formers.It results from little covalent contribution in their nature, which is deduced from the positive V 2 (r(r c )) combined with the slightly negative H(r c ) and moderate r(r c ). 62 For the NH 3 /SiF 4 TtB complex, the electron density of the N/Si TtB is 58.3 × 10 −3 a.u (see Table 4) at MP2/aDZ, and quite consistent with the past works. 3,15A direct connection between N and Si is observed in its topology derived from AIM analysis, conrming the N/Si TtB existence, as also found in the SiF 4 -NCLi complex. 17Nevertheless, the CF 4 -NCH and SiF 4 -NCH complexes were pointed out to exhibit three F/N bonds, instead of the N/Si TtB. 17 The H(r c ) at BCP of N/Si TtB is −0.017 a.u, implying its covalent character in nature, which is consistent with the suggestion of Marín-Luna et al. at MP2/aug ′cc-pVTZ. 15he N/S ChalB in the staggered conformer embraces a slightly higher electron density than that in eclipsed one by 7.3 × 10 −3 a.u, demonstrating the better strength of this ChalB in staggered conformer.For the NH 3 /FCl complex, the r(r c ) at BCP of N/Cl HalB is even higher than the criteria for noncovalent interactions with partial covalent character, recently suggested by Kumar et al. 62 The 2D representations derived from the NCIplot of investigated complexes (Fig. 4) quantitatively reveal different strengths of four noncovalent interactions N/Z (Z = Si, P, S, Cl).In all cases, the negative l 2 displays troughs with electron density ranging from over 0.01 to over 0.06 a.u, suggesting the attractive interactions in these complexes. 37 light bluish region was observed over the NH 3 -PF 3 complex and consistent with the work of Chandra et al. 20 The NCIplot of S/N ChalB in NH 3 -SF 2 is analyzed for the rst time in this study.It shows two well-dened troughs in 2D-graph of both NH 3 -PF 3 and NH 3 -SF 2 .It is strange that AIM did not recognize the smaller interaction rationalizing the small trough.In such a case, the existence of BD(N/Si) bonding orbital indicates that the Si/N bond engages in a covalent interaction or has some covalent nature.

Natural bond orbital analysis
The N/P PniB of H 3 N/PF 3 complex is characterized by three delocalization steps associated with the electron transfer from LP(N) to BD*(P-F a ) (in-plane, 17.82 kJ mol −1 ) and two BD*(P-F b ) (out-plane, z4.90 and 4.98 kJ mol −1 ).Two later processes are expected to strengthen further the stability of the complex.However, Alkorta et al. stated only one delocalization step LP(N) / BD*(P-F) of 12.9 kJ mol −1 at B3LYP/aug ′ -cc-pVTZ. 19The delocalization from the lone pair of nitrogen to s*(S-F) anti-bonding states an energy of 84.18 kJ mol −1 .This value is higher than the work of Otilia Mó et al. using G4 + MP2 correlation. 56In addition, a secondary delocalization LP(N) / BD*(F b -S) is found at 12.51 kJ mol −1 , in consistence with the NCIplot of the second weak interaction found in this complex.Regarding the HalB model, surprisingly, the LP(N) / BD*(F a -Cl) governs the NH 3 /ClF complex with a large E (2) energy of 233.17 kJ mol −1 , implying the high contribution of covalent character in this kind of interaction.Fig. 5 Correlation between the interaction energies and other strength indicators for investigated noncovalent interactions.
In addition, the NBO/NRT-based description of noncovalent interactions helps to quantitatively determine the bond order and valency, which is closely related to classical resonance theory concepts.The total bond orders, which include the covalent and ionic contribution of N/Z interactions (Z = Si, P, S, Cl), are included in Table 5.As expected, herein the high covalent character of N/Si TtB and N/Cl HalB is observed, which account for 18.57 and 27.53% of the total values, respectively.Noteworthy, the covalent contribution to total bond order dominantly controls the strength of the corresponding interactions since the covalent percentage varies in the same trend with the interaction stability.
To determine the best descriptors of bond strength, we plot the trend derived from different descriptors, namely, electrostatic potentials of isolated nucleophilic fragments, local stretching force constants, electron densities at BCPs, and 2 nd -perturbation energies against the change in E int of the noncovalent interactions of interest (Fig. 5).The local stretching force constantk, is recently recognized as an intrinsic characteristic of molecules that directly and accurately measures the bond strength.Meanwhile, the three remaining properties are traditional indicators utilized to characterize chemical bond strength, yet with some degree of discrepancy.According to Fig. 5, it can be seen that the force constants of the local Z/N stretching modes can effectively reproduce the trend obtained from E int .The electrostatic potential and the 2 nd perturbation energy could also qualitatively describe the strength of these weak interactions to a reasonable extent.However, the electron density at BCP derived from Bader's theory shows its poor capacity in presenting the order of interaction strengths.Therefore, it could be concluded that the local stretching force constant is the most accurate descriptor for the strength of these noncovalent interactions.

Conclusion
In this study, various types of s-hole interactions are revisited and thoroughly investigated using high-level quantum chemical methods.The binding energies of complexes between NH 3 and typical Lewis acids (SiF 4 , PF 3 , SF 2 , and ClF) at CCSD(T)/CBS level cover a range of −12.5 to −29.5 kJ mol −1 .Among these complexes, the NH 3 -ClF HalB dimer was found to be the most stable structure.Notably, the strength order of these interactions deviates from the typical trend when the electron acceptor goes from SiF 4 to ClF.Instead, the order is as follows: N/Si TtB > N/Cl HalB > N/S ChalB > N/P PniB, as derived from the analyses of interaction energies and their local stretching force constant.
Besides the supermolecular approach, the high-order SAPT2+(3)dMP2 accurately calculates the interaction energy and conrms the primary contribution of electrostatic components in stabilizing the complex.For other typical approaches, while the bond strength based on E (2) of NBO is effective, the electron density-based ones, i.e., NCIplot and AIM, do not provide accurate results on their stability.The molecular electrostatic potential is recognized as adequate for predicting equilibrium geometries, as well as the strength of noncovalent bonds.
The intrinsic features of noncovalent interactions were also investigated.Upon complexation, the NH 3 -ZF n (Z = Si, P, S, Cl; n = 1-4) are characterized by the local stretching frequencies of 351, 126, 167, and 261 cm −1 at MP2/aTZ level of theory, as Z goes from Si to Cl, respectively.The topological parameters indicate that the investigated N/Si TtB and N/Cl HalB are partly covalent in nature.The NBO-based NRT analysis conrms this nding, showing that the covalency contributions of these TtB and HalB are 18.57% and 27.53%, respectively, in terms of total bonded order.Finally, among different approaches applied, the force constant of the local N/Z stretching vibration is shown to be most accurate descriptor for the strength of noncovalent interactions.The results obtained from this study could provide valuable information for various chemistry disciplines, including supramolecular chemistry, host-guest interactions, as well as crystal engineering, and rational drug design.
Noncovalent interactions r(r c ) V 2 (r(r c )) H(r c )a r(r c ) are in ×10 −3 a.u, V 2 (r(r c )) and H(r c ) are in a.u.
Fig.42D scatter plots and 3D isosurface maps of investigated complexes obtained from the NCI analyses (the NCI color scale is −0.07 < r < 0.07 a.u for SCF densities).

Table 1
25nding energies of noncovalent complexes at various levels of theory (E b , kJ mol −1 ) a of F-Cl and Cl-N, respectively.25Thebinding energy of H 3 N-ClF is computed at −36.6 kJ mol −1 at MP2/aTZ and −34.7 kJ mol −1 at CCSD(T)/CBS, surpassing that of the H 3 N-ClF hydrogen-bonded structure (−1.38 kJ mol −1 at MP2/aTZ, cf.Fig. S2 †).This result is in good agreement with the E b value calculated at MP2/6-311++G(d,p) by Alkorta et al. (−8.86 kcal mol −1 z −37.07 kJ mol −1 a Values in parentheses are E b with only ZPE correction.b The ZPE and BSSE corrections were calculated at MP2/aTZ.c ZPE corrections were calculated at MP2/aTZ.distances

Table 3
Selected structural parameters of complexes optimized at MP2/aTZ a H 3 N-SiF 4 TtB H 3 N-PF 3 PniB H 3 N-SF 2 ChalB Bond distances in mÅ, frequencies in cm −1 , angles in degree, local stretching force constant k in mdyn Å −1 . a

Table 4
Selected parameters at BCPs of typical noncovalent interactions in investigated complexes (density at MP2/aDZ) a